Charge Transport At Liquid/Liquid Interface Hadi J. M. Al-Agealy Adil A. M. Al-Saadi Dept. of Physics/College of Education for Pure Science (Ibn Al-Haitham)/ University of Baghdad Received in:24 June 2012 , Accepted in :15 October 2012 Abstract Charge transfer (CT) at liquid/liquid interfaces are described theoretically depending on the quantum theory .A model that derived used to calculate the rate constant of transport at liquid/liquid interfaces. The calculation of the rate constant of charge transfer depends on the calculation of the reorganization energy, driving force ,and the coupling coefficient . Large reorganization energies and large rate constant for charge transfer ,indicate that the transitions involve more energy to happen . The system have large 𝐸0 (𝑒𝑉) refers that type of liquid is more reactive media than other liquid types with same donor. Driving force energy to drive the charge increases with the increase of absorption energy and decrease of in wave length. Height barrier at liquid/liquid interface that decreasing with decreasing the driving force energy and increasing the absorption energies .Charge transfer is so much small as a barrier of large values but in the low values of barrier ,the transfer is most probable. The large height barrier exclusion transfers across liquid/liquid system and the charger suffers from much resistant to transfer . However, this excluded transfer could be significantly large for high barrier and small concentrations .The theoretical values of rate constant of charge transfer show a good agreement with some of the experimental studies. Key Word: Charge Transfer, Liquid/Liquid interface. 94 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Introduction Charge transfer (CT) reaction is one of the most important processes in chemistry and biology. It has been the subject of lively investigation recently. In the past 30 years, both experiment and theory of charge transfer have made tremendous progress [1] . In simple terms, an electron transfer reaction involves the transfer of an electron from a 'donor'|𝐷 > to an 'acceptor'|𝐴 > state .[2].Since no chemical bonds are broken or formed in the transfer and further more the changes in the bond lengths and angles are rather small .As a result ,the donor becomes oxidized and the acceptor will be reduced to the redox reactions .Redox reactions play an important role in everyday life, for example, the sequence of reactions which sustain the metabolism in plants and animals consists entirely of redox reactions[3] . Since the late 1940 s, the field of (CT) processes have grown enormously, both in chemistry and biology. The development of the field of the (CT) is experimental and theoretical, as will as its relation to the study of other kinds of chemical reactions [4]. The charge transfer is of highly importance in bioenergetics and is an active field of research. Much attention has been devoted to study the charge transfer at liquid /liquid interface and molecular transport reaction processes [5] The classical transfer theory was initially generalized for the liquid |liquid interface considered the charge transfer reaction as asides of steps, where the formation of a precursor complex of the reactants is followed by reorganization of the precursor, charge transfer and dissociation of the products [6]. liquid/liquid system theoretically uses quantum mechanics ;this will be atransfer rate constant which is calculated. Theoretical Framework For the system liquid-liquid interface, we can suppose two localized quantum states |𝛷𝐷𝐿> ,and |𝛷𝐴𝐿>, donor and acceptor liquid state .The time dependent wave function at one dimensional quantum system is [7]. |𝛷(𝑟,𝑡)>=∑ |𝛷(𝑟) ∞0 > 𝑒 −𝑖 ħ 𝐸𝑇…… …………………....................... (1). Where|𝛷(𝑟)>is the basis of the state vector in a Hilbert space. The model Hamiltonians used to describe the electron transfer dynamics comprise of several parts that have well defined physical origins. The full Hamiltonian ,𝐻, is spilt into the donor liquid,𝐻𝐷𝐿,acceptor liquid, 𝐻𝐴𝐿 and time dependent term which describes the interaction 𝐻𝐷𝐴𝐿 [8]. 𝐻 = 𝐻𝐷𝐿 + 𝐻𝐴𝐿 + 𝐻𝐷𝐿𝐴𝐿 = 𝐻0 + 𝐻𝐷𝐿𝐴𝐿 ……………..................(2) Where 𝐻0 is the time independent of the unperturbed system, the condition on the perturbation 𝐻𝐷𝐿𝐴𝐿 is relaxed to permit it to vary in time. In terms of orthonormal set 𝛷𝑘(𝑟) which satisfies [9]. 𝐻0𝛷𝑘(𝑟)=Ek𝛷𝑘(𝑟) ……………………………………………..(3) Then the probability of electron transition from donor liquid state to acceptor liquid state is given by [10]. 𝑊𝐷𝐿𝐴𝐿 = 2𝜋 ħ |𝑇𝐷𝐿𝐴𝐿|2𝛿(𝐸𝐷𝐿 − 𝐸𝐴𝐿 − ħ𝜔) ………………. ………………….(4). Then the rate constant is given by with density [11]. 𝛫ET 𝐿/𝐿 = 2π ħ |𝑇𝐷𝐴|2 ρ(EA _ED) ……………………….. …… …….(5) Rate transfer Eq. (5) with density becomes. 𝛫ET 𝐿/𝐿 =2𝜋 ħ |𝑇𝐷𝐴| 2 N 𝑒 −(𝐸0+Δ𝐺0) 2 4𝐸0𝑘𝐵𝑇 …………………………………… (6) But N(𝜋 𝛽 ) 1 2 = 1 ⇒ N = (𝛽 𝜋 ) 1 2=( 1 4𝜋𝐸0𝑘𝐵𝑇 ) 1 2 …………………………….(7) Eq. (6) with Eq. (7) is written 95 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 𝛫ET 𝐿/𝐿=2𝜋 ħ | TDA|2 ( 1 4𝜋𝐸0𝐾𝐵𝑇 ) 1 2 𝑒𝑥𝑝 −(𝐸0+Δ𝐺0) 2 4𝐸0𝑘𝐵𝑇 ……………………… (8). Where ℏ = ℎ 2𝜋 is the ℎ Planck constant,𝑘𝐵 is the Boltzmann constant, 𝑇 is the absolute temperature and 𝑇𝐷𝐴 is the coupling matrix element. When the liquid/liquid system absorption photon light to excite according to expression [12]. ∆𝐺 𝜊 = ℎ𝜈 − 𝐸0 ………………………………………………….(9) Where ∆𝐺0 is the effective free energy (driving force) is given by [13] .∆𝐺 𝜊 = ℎ� 𝑐 𝜆 � − 𝐸0 ………………………………………………(10) Where 𝜈 is the frequency, c is the velocity of light and 𝜆 is the wave length .Also 𝐸0 is contribution of the reorganization energy due to reaction, can be written as [14] . 𝐸0 = (Δ𝑒)2 4𝜋𝜖0 � 1 2𝑎1 + 1 2𝑎2 − 1 𝑅 �� 1 𝜖1 𝑜𝑝+𝜖2 𝑜𝑝 − 1 𝜖1 𝑆+𝜖2 𝑆�…………………….…(11) Where 𝑅 = 𝑎1 + 𝑎2 is the separation distance between the two reactants and 𝑎1, 𝑎2 are the radii of ions,𝜖𝑜𝑝 𝑎𝑛𝑑 𝜖𝑠 refers to the optical and static dielectric constant of two liquid .The radii of donor and acceptor can be estimated from the apparent molar volume using spherical approach[ 15]. 𝑎𝑖 = � 3𝑀𝑊 4𝜋𝑁𝐴𝜌 � 1 3……………………………………………………....(12) Where 𝑎𝑖 is the radius of donor or acceptor, Avogadro's number construes 𝑁𝐴, MW is the molecular weight , and 𝜌 is the mass density of liquid. Results A quantum theory have been used to study and calculate the transitions of electron rate constant at liquid/liquid system . The calculation of the rate constant of electron transfer is dependent on the calculation of the reorganization energy , the electronic coupling, and the driving force energy . One first step to calculate the reorganization energy . 𝐸0(𝑒𝑉) that can be calculated theoretically using Eq.(11 ).To calculate the reorganization energies 𝐸0(𝑒𝑉) for water/liquid system, one can estimate the radius for donor (water) and acceptor liquid using Eq.(12) , substation the values of Avogadro's construes 𝑁𝐴 = 6.02 × 1023 𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑒 𝑚𝑜𝑙 molecular weight MW ,and Density mass 𝜌 for all liquids from table (1) in Eq.(12 ),result are listed in table (2 ) . Inserting in Eq. ( 11) the values of radii of donor and accepter , dielectric constant 𝜖𝑠 optical dielectric constant 𝜖𝑜𝑝 from table (1) and assume the distance 𝑅 = 𝑎𝐷 + 𝑎𝐴 between center to center for donor and acceptor, knowing that 𝑒 2 4𝜋𝜖 = 14.4 𝑒𝑉 the results of reorganization free energy have been summarized in table (3 ) . On the otherhand, we can calculate the driving force energy ( free energy) term at the liquid/liquid interface as a function of the reorganization energy ,and the absorption energy using Eq.(10). The absorption energy in Eq.(9) can be roughly taking from the wave length in visible spectrum(4000𝐴°-7000 𝐴° ) and transform energy equation 𝐸 = ℎ𝜈 =ℎ𝑐 𝜆 Where h is Planck constant ,c is the velocity of light ,and 𝜆 is the wave length . Since we have considered that the absorbed visible light is directed to the aqueous phase .we evaluated the driving force energy for liquid/liquid system by inserting the values of the reorganization energy from table(3),and absorption energy from spectrum in Eq.(8),results are listed in table(4).Next ,we calculate the rate constant using Eq.(7), by feedback in a Math lab program the results of both reorganization energy are from table(3), driving force energy is in table (4), and using the coupling coefficient (200 ,400 )cm-1[5],results are summarized in tables (5) to (6). 96 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Discussion First-order perturbation theory and quantum theory treatment have been used to drive an expression to the transitions of electron rate constant at liquid/liquid system .Rate constant of charge transfer depends on many parameters such that :the reorganization energy, driving force energy ,height barrier ,and coupling coefficient. In this paper we will calculate the rate constant for charge transfer at liquid/liquid interface system depending on the results of the reorganization energies and the driving free energy (driving force ). The exponential in Eq.( 8) have tested the probability of the transfer of charge from donor water to liquid acceptor state. The reorganization of free energies is calculated depending on the semi classical model for charge transfer at liquid/liquid interface system using a two spherical model based on the Marcus theory of charge transfer (CT) . Table(3) shows that the reorganization energy for charge transfer at liquid-liquid system indicates that is in general whenever there is an increase in the dielectric constant for acceptor, there is increase in the reorganization energies lead to an increases in rate of charge in tables (5) and (6) respectively and vice versa , similarly whenever, there is an increase in the interface index for acceptor liquid leads to a decrease in the reorganization energies for system with the same refractive index and dielectric constant for the donor resulted to decrease in rate of charge transfer . This indicates that the reorganization energy as a function of the polarity 𝑓(𝑛, 𝜖) = � 1 𝜖𝑜𝑝 − 1 𝜖𝑠 � for system, this means that a small polarity function results to a decrease in the reorganization energy and vice versa. Comparison of the results of calculation of the reorganization energy 𝐸0 are in table ( 3) and the rate of charge transfer is in table(5)and(6),indicates that the charge transfer is more probable in liquid-liquid system have more polarity parameter for example water/formic acid have 𝑓(𝑛, 𝜖) ≅ 0.2657 leads to large reorganization energy 𝐸0 ≈ 0.898 𝑒𝑉. Notably the charge transfer in the system that have large dielectric constant is stronger than the system have that a small dielectric constant. Our results showed agreement with experimental value for 𝐸𝑂 [16 ]. Next the results of driving force showed that table(4) gives the results of the driving force energy for charge transfer take term accounting for the attractive interactions between the tails of the donor state wave function and acceptor state wave function. Results in table (4) of driving force Δ𝐺0(eV), show that energy that is taken to bring the donor and acceptor together and is the part of the work broken to derive the charge to transfer from donor to acceptor. The driving force energy to drive the charge increases with the increase of absorption energy and decreases in wave length. The exponential in rate describing the barrier height is the function of both reorganization energy and driving force .Decreasing barrier leads to increase the transfer of charge cross liquid/liquid interface with a decrease of the driving force energy and increase the absorption energies .This indicates the absorption energy is divided into reorientation of the system to transfer and the other enables to drive the charge to transfer due to potential barrier height from donor to acceptor. Again, the transition is so much small as a barrier large values but in the low values of barrier ,the transfer is most probable the large height barrier exclusion transfer across liquid/liquid system and the electron suffering much resistant to transfer . However, this excluded transfer could be significantly lower for high barrier and small concentrations of charge because of the hard (large height ) barrier overlapping effect .The theoretical result as well as with the other results[ 2 ]. Conclusions In this study ,it can be concluded depending on our results of calculation that the rate of charge transfer is more probable happen and stronger depends on the reorganization and driving force energies . The reorganization energy depends on three parameter dielectric 97 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 constant, optical properties (refractive index n )and polarity .It has shown that all donor molecular have large dielectric constant ,have large reorganization energies and large rate constant for charge transfer ,indicates that the transitions involve more energy to happen . On the otherhand the system have large 𝐸0 (𝑒𝑉) refers that type of liquid is more a reactive media than other liquid type with the same donor. The driving force energy for charge transfer takes term accounting for the attractive interactions between the tails of the donor state wave function and acceptor state wave function and depends on the reorganization energy and the absorption energy visible spectrum. Its energy that is taken to bring the donor and acceptor together and drive the charge increases with the increase of absorption energy and decrease in wave length .Height barrier at liquid/liquid interface that decreases with the decrease of the driving force energy and increases the absorption energies . This indicates that the absorption energy is divided into reformation the system to transfer and the other enables to drive the charge to transfer due to potential barrier height from donor to acceptor. It can be concluded that the transition is so much small as barrier large values but in the low values of barrier ,the transfer is most probable the large height barrier exclusion transfer across liquid/liquid system and the charger suffers much resistant to transfer . However, this excluded transfer could be significantly lower for high barrier and small concentrations of charge because of the hard (large height ) barrier overlapping effect . References 1-Jing,M. C; TongIng, H.and Chung-Yuan .M,(1990) Experimental Investigation of Excited-State Electron-Transfer Reaction: Effects of Free Energy and Solvent on Rates, J. Phys. Chem, 94, 2889-2896 2- Kavarnos, J. G.(1993) Fundamentals of Photoinduced Electron Transfer, VCH Publishers, Inc., New York ISBN 0-89573-75 1-5. 3-Hussein,K.M.(2011)Study of The Electron Transfer At Metal/Semiconductor Interface By Using Quantum Mechanical Theories,MS.c Thesis. University of Baghdad. 4-Mohsin, A. H.(2009)A theoretical model for electron transfer in Dye/Semiconductor system interface with verity solvents, MS.c thesis, Baghdad university. 5-Xiaoquan ,L .Q W.and Xiuhui, L.(2007)Review: Recent Applications Of Scanning Electrochemical Microscopy To The Study Of Charge Transfer Kinetics, Analytical Chemical Acta 601,10-25. 6-Christoffer, J. (2003)Electro deposition and reactions at liquid-liquid interfaces, Ph.D., Helsinki University of Technology Department of Chemical Technology Laboratory of Physical Chemistry and Electro chemistry. 7-Itzhak,B. (2005)Quantum mechanics, Book ,3ed ,Wily &Sons. publisher. 8-Al-Agealy, H.J.M.and Hassooni, M.A.(2011)Calculate of The Rate Constant of Electron Transfer In Tio2-Safranine Dye SystemIbn Al-Hatham J.For Pure &Appl.Sci.,24,3. 9- Garrison, J. C.and Chiao, R. Y. (2008)Quantum Optics ,Book, Oxford University Press Published in the United States by Oxford University Press Inc., New York 10-Jan, G. K ,and Andreas, G. (2002).Semiconductors For Micro And Nanotechnology—An Introduction For Engineers,Wiley-Vch Verlag Gmbh, Weinheim microscopy to the study of charge transfer kinetics,analytica chemical acta 6 0 1 10–25] 11-Adil,A.AL-saadi (2012) Interface Charge Transfer in liquid/liquid ,M.Sc. thesis, collage education Ibn Al-Haitem.Baghdad university. 12- Al-agealy, H. J M.( 2008) photo induced electron transfer between metal lop orphyrin complex dihydroxy antimony tetraphenylporphine and halide in acetonitrile solution" Ibn –Al Hiatham J.for pure and appl. Sci.21(1): 34-44. 13- Al-agealy,H.J. M.and Hadi, A. Z. (2008),ET between ketone triplets and organic dyes in variety solvent, J. of the college of basic education, 64,16. 98 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 14- Al-agealy,H.J.M. and Adil,A.M.AL-Saadi (2013) Theory and Calculation of The Reorganization Energy of Electron Transfer at Liquid/Liquid Interface, Ibn –Al Haitham J.for Pure & Appl. Sci.26: (2). 15- Al-agealy H. J. M.., and Hasoony,M. A. (2010)A Theoretical Study of The Effect of The Solvent Type on The Reorientation Energy of Dye/Semiconductor System Interface", Ibn Al-Haitham J. For Pure & Appl. Sci. 23(3) 51-57. 16-Wibren ,D.O. (.2002)Electron transfer donor –Bridge-acceptor system and derived material. Ph.D. thesis, Debye Institute and University of Utrecht.chapter (1)1 -10. ISBN 90- 393-3095-6. 17-Greenwood, N. N.and Earnshaw, A.(1997) Chemistry of the Elements, 2nd edition., Butterworth-Heinemann, Oxford, UK. 18- Wells,A. F.(1984) 'Structural Inorganic Chemistry, 5th edition., Oxford University Press, Oxford, UK. 19-Silberberg,M. S.( 2009). Chemistry, Book, 5th edition, McGraw-Hill. Publisher. 20-West,R.C.(1995)."Handbook of chemistry and physics".76th edition.CRC. press:Boca Raton.FL. 21-Paul,W.;Derek,M.D;David,J.G.;Christopher;J.C., and Donald G.T.(2010)Minnesota Solvent Descriptor Database, Department of Chemistry and Supercomputer Institute, University of Minnesota,Minneapoils.MN 55455-0431. Table No.(1):Characteristic of liquid material Liquid Type Molecule weight (MW) 𝒈. 𝒎𝒐𝒍−𝟏 [17,18,19] Density (𝛒𝛒) 𝒈. 𝒄𝒎−𝟑 [17,18,19] Dielectric Constant 𝝐𝒔 [20,21] Refractive index (n) [20,21] Water 18 1 80 1.333 Acetone 58.08 0.791 20.493 1.3588 Formic acid 46.03 1.22 51.1 1.3714 Bromoform 252.73 2.889 4.2488 1.6005 Chloroform 119.38 1.483 4.7113 1.4459 N-methylformamide 59.07 1.003 181.59 1.4319 N,N dimethylformamide 73.09 0.944 37.219 1.4305 Ethanol 46.0414 0.790 24.852 1.3611 n-hexadecane 226.44 0.733 2.0402 1.4345 Haxanic acid 116.16 0.93 2.6 1.4163 1,2 ethanediol 63 1.1151 40.245 1.4318 99 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Table No.(2):The theoretical calculation values of radii 𝑎𝑖(𝐴°) for donor and acceptor liquid Liquid Type Molecule weight 𝒈. 𝒎𝒐𝒍−𝟏 [17,18,19] density 𝒈. 𝒄𝒎−𝟑 [17,18,19] radii𝑎𝑖(𝑨 𝟎) Water 18 1 1.92520792 Acetone 58.08 0.791 3.076121696 Formic acid 46.03 1.22 2.463847665 Bromoform 252.73 2.889 3.261043233 Chloroform 119.38 1.483 3.171881441 N-methylformamide 59.07 1.003 2.858087259 N,N dimethylformamide 73.09 0.944 3.13099322 Ethanol 46.0414 0.790 2.848135287 n-hexadecane 226.44 0.733 4.96595975 Haxanic acid 116.16 0.93 3.672073423 1,2 ethanediol 63 1.1151 2.818787796 Table No.(3):Our calculation results of reorganization free energy 𝑬𝟎 (𝒆𝑽) for change transfer at Water\Liquid interface system. System Dielectric constant for acceptor 𝝐𝒔 [20,21] Optical dielectric constant for acceptor 𝝐𝒐𝒑 Reorganization free energy 𝑬𝟎 (𝒆𝑽) Water/Acetone 20.493 1.84633744 0.8516752339 WaterFformic acid 51.1 1.88073796 0.8986405084 Water/Bromoform 4.2488 2.56160025 0.6932973949 Water/Chloroform 4.7113 2.09062681 0.7858438989 Water/N,Methylformamide 181.59 2.05033761 0.8363805396 Water/N,Ndimeethylformamide 37.219 2.04633025 0.8075301745 Water/Ethanol 24.852 1.85259321 0.8635918533 Water/n-hexadecane 2.0402 2.05779025 0.8246426859 Water/Hexanic acid 2.6 2.00590569 0.8118435171 Water/1,2 ethanediol 40.245 2.05005124 0.8244227082 100 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Table No. (4 ):The result of our calculation of driving force energy ∆𝑮𝒐(𝒆𝑽)for charge transport in Water/Liquid system. Driving force energy ∆𝑮𝒐(𝒆𝑽) W av e le ng th 𝝀 ( 𝑨 °) W at er -b ro m of or m W at er -n -h ex ad ec an e W at er -c hl or of or m W at er - N ,N di m et hy lf or m am id e W at er -h ax an ic a ci d W at er -1 ,2 et ha ne di ol W at er -n -m et hy lf or m am id e W at er -A ce to ne W at er -e th an ol W at er -F or m ic a ci d 4000 2.4127 2.2813 2.3201 2.2984 2..2941 2.2815 2.2696 2.2543 2.2424 2.2073 4500 2.0676 1.9362 1.9750 1.9533 1.9490 1.9364 1.9245 1.9092 1.8973 1.8622 5000 1.7915 1.6601 1.6989 1.6772 1.6729 1.6603 1.6484 1.6331 1.6212 1.5861 5500 1.5656 1.4342 1.4730 1.4513 1.4470 1.4344 1.4225 1.4072 1.3953 1.3602 6000 1.3774 1.2460 1.2848 1.2631 1.2588 1.2462 1.2343 1.2190 1.2071 1,1720 6500 1.2181 1.0867 1.1255 1.1038 1.0995 1.0869 1.0750 1.0597 1.0478 1.0127 7000 1.0816 0.9502 0.9890 0.9673 0.9630 0.9504 0.9673 0.9232 0.9113 0.8762 Table No.(5):Results of the electron transfer rate constant at Water/Liquid interface system with coupling coefficient 𝑻𝑫𝑨 = 𝟐𝟎𝟎 𝟖𝟎𝟔𝟓.𝟓𝟐 = 𝟎. 𝟎𝟐𝟒𝟕𝟗𝟔𝟗 (eV). W av e le ng th 𝝀 ( 𝑨 °) Rate constant 𝛫ET 𝐿/𝐿 (sec-1) W at er -b ro m of or m W at er -n -h ex ad ec an e w at er -c hl or of or m W at er -N ,N di m et hy lf or m am id e W at er -h ax an ic a ci d W at er -1 ,2 e th an ed io l W at er - N ,m et hy lf or m am id e W at er -A ce to ne W at er -e th an ol W at er -F or m ic a ci d 4000 4.562 ×𝟏𝟎−𝟒𝟖 1.788 ×𝟏𝟎−𝟑𝟖 3.807 ×𝟏𝟎−𝟒𝟏 1.530 ×𝟏𝟎−𝟑𝟗 2.871 ×𝟏𝟎−𝟑𝟗 1.751 ×𝟏𝟎−𝟑𝟖 9.183 ×𝟏𝟎−𝟑𝟖 7.343 ×𝟏𝟎−𝟑𝟕 3.428 ×𝟏𝟎−𝟑𝟔 2.641 ×𝟏𝟎−𝟑𝟒 4500 2.20 8×𝟏𝟎−𝟑𝟓 8.226 ×𝟏𝟎−𝟐𝟖 8.845 ×𝟏𝟎−𝟑𝟎 1.184 ×𝟏𝟎−𝟐𝟖 1.947 ×𝟏𝟎−𝟐𝟖 8.123 ×𝟏𝟎−𝟐𝟖 3.007 ×𝟏𝟎−𝟐𝟕 1.548 ×𝟏𝟎−𝟐𝟔 5.209 ×𝟏𝟎−𝟐𝟔 1.605 ×𝟏𝟎−𝟐𝟒 5000 2.614 ×𝟏𝟎−𝟐𝟔 3.492 ×𝟏𝟎−𝟐𝟎 8.946 ×𝟏𝟎−𝟐𝟐 7.293 ×𝟏𝟎−𝟐𝟏 1.089 ×𝟏𝟎−𝟐𝟎 3.462 ×𝟏𝟎−𝟐𝟎 9.963 ×𝟏𝟎−𝟐𝟎 3.755 ×𝟏𝟎−𝟏𝟗 1.001 ×𝟏𝟎−𝟏𝟖 1.603 ×𝟏𝟎−𝟏𝟕 5500 1.353 ×𝟏𝟎−𝟏𝟗 1.539 ×𝟏𝟎−𝟏𝟒 7.476 ×𝟏𝟎−𝟏𝟔 4.218 ×𝟏𝟎−𝟏𝟓 5.887 ×𝟏𝟎−𝟏𝟓 1.525 ×𝟏𝟎−𝟏𝟒 3.652 ×𝟏𝟎−𝟏𝟒 1.091 ×𝟏𝟎−𝟏𝟑 2.461 ×𝟏𝟎−𝟏𝟑 2.426 ×𝟏𝟎−𝟏𝟐 6000 1.719 ×𝟏𝟎−𝟏𝟒 3.006 ×𝟏𝟎−𝟏𝟎 2.379 ×𝟏𝟎−𝟏𝟏 1.018 ×𝟏𝟎−𝟏𝟎 1.344 ×𝟏𝟎−𝟏𝟎 2.992 ×𝟏𝟎−𝟏𝟎 6.227 ×𝟏𝟎−𝟏𝟎 1.561 ×𝟏𝟎−𝟗 3.084 ×𝟏𝟎−𝟗 2.104 ×𝟏𝟎−𝟖 6500 1.621 ×𝟏𝟎−𝟏𝟎 6.586 ×𝟏𝟎−𝟕 7.621 ×𝟏𝟎−𝟖 2.629 ×𝟏𝟎−𝟕 3.333 ×𝟏𝟎−𝟕 6.582 ×𝟏𝟎−𝟕 1.224 ×𝟏𝟎−𝟔 2.679 ×𝟏𝟎−𝟔 4.771 ×𝟏𝟎−𝟔 2.440 ×𝟏𝟎−𝟓 7000 2.297 ×𝟏𝟎−𝟕 2.948 ×𝟏𝟎−𝟒 4.605 ×𝟏𝟎−𝟓 1.343 ×𝟏𝟎−𝟒 1.636 ×𝟏𝟎−𝟒 2.935 ×𝟏𝟎−𝟒 5.020 ×𝟏𝟎−𝟒 9.859 ×𝟏𝟎−𝟒 1.640 ×𝟏𝟎−𝟑 6.599 ×𝟏𝟎−𝟑 101 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Table No.(6):Results of the electron transfer rate constant at Water/Liquid interface system with coupling coefficient 𝑻𝑫𝑨 = 𝟒𝟎𝟎 𝟖𝟎𝟔𝟓.𝟓𝟐 = 𝟎. 𝟎𝟒𝟗𝟓𝟗𝟑𝟖(eV). W av e le ng th 𝝀 ( 𝑨 °) Rate constant 𝛫ET 𝐿/𝐿 (sec-1) W at er -b ro m of or m W at er -n -h ex ad ec an e w at er -c hl or of or m W at er -N ,N di m et hy lf or m am id e W at er -h ax an ic a ci d W at er -1 ,2 e th an ed io l W at er -N ,m et hy lf or m am id e W at er -A ce to ne W at er -e th an ol W at er -F or m ic a ci d 4000 1.839 ×𝟏𝟎−𝟒𝟕 7.209 ×𝟏𝟎−𝟑𝟖 1.535 ×𝟏𝟎−𝟒𝟎 6.125 ×𝟏𝟎−𝟑𝟗 1.149 ×𝟏𝟎−𝟑𝟖 7.010 × 𝟏𝟎−𝟑𝟖 3.675 ×𝟏𝟎−𝟑𝟕 2.938 ×𝟏𝟎−𝟑𝟔 1.372 ×𝟏𝟎−𝟑𝟓 1.057 ×𝟏𝟎−𝟑𝟑 4500 8.902 ×𝟏𝟎−𝟑𝟓 3.316 ×𝟏𝟎−𝟐𝟕 3.540 ×𝟏𝟎−𝟐𝟗 4.739 ×𝟏𝟎−𝟐𝟖 7.793 ×𝟏𝟎−𝟐𝟖 3.251 ×𝟏𝟎−𝟐𝟕 1.203 ×𝟏𝟎−𝟐𝟔 6.197 ×𝟏𝟎−𝟐𝟔 2.084 ×𝟏𝟎−𝟐𝟓 6.424 ×𝟏𝟎−𝟐𝟒 5000 1.053 ×𝟏𝟎−𝟐𝟓 1.408 ×𝟏𝟎−𝟏𝟗 3.580 ×𝟏𝟎−𝟐𝟏 2.919 ×𝟏𝟎−𝟐𝟎 4.360 ×𝟏𝟎−𝟐𝟎 1.385 ×𝟏𝟎−𝟏𝟗 3.987 ×𝟏𝟎−𝟏𝟗 1.5030 ×𝟏𝟎−𝟏𝟖 4.009 ×𝟏𝟎−𝟏𝟖 6.437 ×𝟏𝟎−𝟏𝟕 5500 5.457 ×𝟏𝟎−𝟏𝟗 6.204 ×𝟏𝟎−𝟏𝟒 2.992 ×𝟏𝟎−𝟏𝟓 1.688 ×𝟏𝟎−𝟏𝟒 2.356 ×𝟏𝟎−𝟏𝟒 6.106 ×𝟏𝟎−𝟏𝟒 1.461 ×𝟏𝟎−𝟏𝟑 4.3692 ×𝟏𝟎−𝟏𝟑 9.851 ×𝟏𝟎−𝟏𝟑 9.709 ×𝟏𝟎−𝟏𝟐 6000 6.931 ×𝟏𝟎−𝟏𝟒 1.212 ×𝟏𝟎−𝟗 9.522 ×𝟏𝟎−𝟏𝟏 4.077 ×𝟏𝟎−𝟏𝟎 5.380 ×𝟏𝟎−𝟏𝟎 1.197 ×𝟏𝟎−𝟗 2.492 ×𝟏𝟎−𝟗 6.247 ×𝟏𝟎−𝟗 1.234 ×𝟏𝟎−𝟖 8.421 ×𝟏𝟎−𝟖 6500 6.538 ×𝟏𝟎−𝟏𝟎 2.655 × 𝟏𝟎−𝟔 3.050 ×𝟏𝟎−𝟕 1.052 ×𝟏𝟎−𝟔 1.334 ×𝟏𝟎−𝟔 2.634 ×𝟏𝟎−𝟔 4.901 ×𝟏𝟎−𝟔 1.072 ×𝟏𝟎−𝟓 1.909 ×𝟏𝟎−𝟓 9.767 ×𝟏𝟎−𝟓 7000 9.262 ×𝟏𝟎−𝟕 1.188 ×𝟏𝟎−𝟑 1.843 ×𝟏𝟎−𝟒 5.375 ×𝟏𝟎−𝟒 6.548 ×𝟏𝟎−𝟒 1.174 ×𝟏𝟎−𝟑 2.009 ×𝟏𝟎−𝟑 3.946 ×𝟏𝟎−𝟑 6.565 ×𝟏𝟎−𝟑 0.0264 102 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 انتقال الشحنة لسطح سائل/سائل ھادي جبار مجبل العكیلي عادل علي منصور السعدي جامعة بغداد/)ابن الھیثم( للعلوم الصرفة كلیة التربیة/قسم الفیزیاء 2012تشرین االول :15قبل البحث في ، 2012حزیران 24 :استلم البحث في الخالصة انتقال الشحنة لسطح سائل/سائل وصفت نظریا اعتمادا على النظریة الكمیة.اآلنموذج المشتق استعمل لحساب ثابت معدل األنتقال لسطح سائل/سائل. حساب ثابت معدل األنتقال للشحنة اعتمد على حساب طاقة اعادة التنظیم،والقوة والمعدل العالي لثابت األنتقال لشحنة یشیر الى ان األنتقاالت تتضمن المساقة،ومعامل الترابط. طاقة الكبیرة العادة التنظیم (طاقة اعادة التنظیم المقاسة باالكترون فولت) عالیة یشیر الى 𝐸0 (𝑒𝑉)مزیدا من الطاقة لتحدث. النظام الذي یملك نوعیة السائل الذي یتفاعل بالوسط اكثر من السوائل األخرى للواھب(المانح) نفسھ.طاقة القوة المساقة والتي تسوق الشحنة یتناقص مع تناقص القوة تتزاید مع زیادة الطاقة الممتصة وبتناقص األطوال الموجیة .ارتفاع البئر لسطح سائل/سائل المساقة مع زیادة الطاقة الممتصة . والشحنة المنتقلة تكون قلیلة الكمیة لقیم عالیة في بئر ما ولكن القیم واطئة لبئر فأن العبور یكون اكثر احتماال منھ.ارتفاع العالي للبئر یحجب االنتقال عبر نظام السائل والشحنة تعاني ممانعة األنتقال .وعلى حال فأن احتجاب العبور یكون ملحوظا لبئر عالي األرتفاع وبتركیز قلیل. القیم النظریة لثابت معدل االنتقال للشحنة اي اظھرت تطابقا مع بعض الدراسات التجریبیة. :أنتقال الشحنة،سطح سائل/سائل.الكلمات المفتاحیة 103 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013